1. Field of the Invention
This invention relates in general to a loudspeaker system and in particular to an improved loudspeaker system which includes two drivers coupled to a horn by means of acoustical coupling networks.
2. Description of the Prior Art
It has been difficult if not impossible in speaker systems of the prior art to eliminate frequency distortion which varies as a function of the radiating angle from the speaker system. Such distortion results from the relationship of the wavelength to the diameter of the piston and in multiple driver systems to the spacing and positioning of the pistons. Although it has been proposed to solve this problem of frequency distortion by having the virtual size of the radiators decrease with frequency such solution has not eliminated frequency distortion as a function of radiating angle. The sound pressure (ignoring distance) radiated by a piston in a plane wall is: EQU p(.theta.) = 2J.sub.1 [ F (.theta.)]/F (.theta.).sup.2 EQU f.theta. = ka sin .theta.
Where .theta. is the angle away from the axis; k = .omega./c; c = velocity of sound in air; and "a"=radius of the piston. J.sub.1 is the type 1 Bessel function of order 1 and argument F (.theta.). This function has the appearance of a damped sinusoid varying with .theta.; thus influencing p (.theta.) proportionally, resulting in directional lobes when ka is large.
Assuming point sources the pressure (ignoring distance) of a number (n) of such sources and at a distance much greater than the extent between them is: EQU p (.theta.) = sin [n .pi. m f sin .theta./c]/[n sin (.pi.m f sin .theta./c)]
Where f is the frequency and m is a factor including the extent between the sources. The function exhibits the periodic nulls characteristic of a sin x/x function. Even when delays are introduced electrically into the factor m, to reduce the frequency variance on-axis, off-axis lobes must still occur.
Thus, in multiple radiator systems it is inevitable and unavoidable that lobes and nulls will appear in the directivity characteristic at any one frequency and that these lobes and nulls will not coincide as frequency is changed. In a monaural music reproduction system, this problem is not too serious if one is positioned reasonably within the coverage angle of the loudspeakers. However, even in this case there will be some frequency distortion if the power response of the speaker does not reasonably follow the response on the listener's axis, since, assuming uniform diffusion, the mean square sound pressure at the listener on sustained signals will be: EQU p.sup.2 (r) = W.rho..sub.o c[1/(4 r.sup.2) + 4/R]
where .rho..sub.o = density of air; R = room constant, a function of room size and acoustic absorption; W = total power emitted by the radiator.
The term 1/(4.pi.r.sup.2) represents the direct sound; however, if the radiator is characterized by the directivity equations, the term becomes Q.sub.D /(4.pi.r.sup.2), where Q.sub.D represents the position of the listener on the lobed direction pattern -- and is frequency variant.
The direct sound term can therefore, as a function of frequency, fall well below the reflected sound term, 4/R, or at least below early reflections, resulting in an unnatural smearing of the frequency components of the sound, both in space and time.
Moreover, in stereo systems, where virtual sources not coinciding with the loudspeaker position must be produced, the problem can be unusually serious.